Probability current density

Equation (7) is an exact analogue of the continuity equation (1.7) of hydrodynamics, and this allows definition of a probability current density... 

If the vector j(r,t) = idca I is interpreted as a probability current density, one has the continuity equation... 

In Section 5.2, we used an expression for the flux operator. In most quantum mechanics textbooks expressions for the probability current density, or probability flux density, are given in terms of the wave function in the coordinate representation. We need an expression for the flux density operator without reference to any particular representation, and since it is rarely found in the textbooks, let us in the following derive this expression. 

S area entropy probability current density Poynting... 

Effects of spatial nonhomogeneity for the probability current density (or a quantum-mechanical current density) in the semiconductor 2D nanostructures in the form of joints in the direction of propagation of the electron wave of narrow and wide rectangular quantum wells have been theoretically studied. 

Figure 1. Contour plots (in the (x-z) plane) of spatial distribution of the normalized probability current density jx (x, z)/ jx (0.0) in the wide QW2 for symmetric (a) and asymmetric (b) structures. The numbers designate amplitudes of peaks in relative units. The painted areas are sections of peaks at heights 0.9 (a) and 0.8 (b) thick lines are sections at heights 0.45 (a) and 0.35 (b) thin lines are sections at heights 0.31 (a) and 0.23 (b).

S area, entropy, probability current density, Poynting... 

The quantum flux operator F measures the probability current density. The latter satisfies the continuity equation resulting from the invariance of the norm of the wave packet in the coordinate basis. For a stationary wave function, the probability density is independent of time and the flux is constant across any fixed hypersurface. In reaction dynamics the flux operator is most generally defined in terms of a dividing surface 0 which... 

The probability current density is obtained from Eq. (30) for the density matrix. 

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